2.3. In vitro – in vivo scaling of an NCE

2.3.2.1. Initial velocity conditions

When the metabolic routes of an NCE are recognised either in liver microsomes or in liver homogenate from the human or the test species, a method for the separation and, if a reference substance is available, quantitation of metabolites is required. Determination of the initial velocity conditions is important for an accurate determination of the enzyme kinetic parameters of metabolite formation reactions. The determination of the IC₅₀ values for CYP-selective diagnostic inhibitors is best performed if the substrate concentration used is selected from within the linear part of the time and protein dependence curve for the metabolite formation from an NCE. When possible, the substrate concentration should be close to the achieved concentrations in vivo or at least close to the K_m value (Guengerich 1995b; Yuan et al. 1999).

2.3.2.2. Apparent enzyme kinetic parameters K_m and Vmax

The determination of apparent enzyme kinetic parameters in human liver preparations with different substrates has been presented in various publications and is also available as teaching material (for example, Boobis 1995), and it will not be considered in detail here. Basically, there are two approaches available for this purpose: 1) the use of graphical presentations and derivations for Michaelis-Menten kinetics and 2) the use of an iterative software for calculating the parameters from untransformed data using the Michaelis-Menten equation. The latter approach is nowadays most widely used, since it gives somewhat more accurate and more reproducible values than the graphical method. Still, the graphical method is also in use and, if properly handled, gives results accurate enough for practical purposes.

2.3.2.3. Prediction of the intrinsic clearance (Cl_int)

For the prediction of intrinsic clearance, one should be familiar with specific information about the enzymes participating in the metabolism of an NCE. This includes the identity of the enzymes and the enzyme-kinetic parameters for the NCE with metabolising enzymes. Without this information, it is still possible to derive K_m and V_max by following substrate consumption. This approach does not reveal the parameters for individual metabolic routes, but allows the prediction of overall intrinsic clearance (Cl_int) and produces information about the bioavailability of the drug under study.

For example, Ito et al. (1998a; 1998b) have studied extensively the quantitative prediction of in vivo drug clearance and drug interactions from in vitro studies. Both publications would be worth an introduction, but are too extensive to be reviewed here.

Basically, the in vitro metabolism can be converted into its in vivo counterpart. From the Michaelis-Menten equation for the velocity (v) of metabolite formation,

when K_m >> [S];, the reductions of the equation lead to the general expression that the intrinsic clearance (Cl_int) is

Cl_int = V_max/K_m, where

V_max/K_m is presented as volume/time. This constant can be compared to the respective in vivo value obtained from pharmacokinetic studies. Obach et al. (1997) presented an extensive survey, where they compared values obtained from in vitro studies of 50 compounds to respective in vivo results. In that study, 12 different methods for clearance predictions were used, of which four were employed to predict values for in vitro half-life (t) and, consequently, to predict clearance, four utilised in vitro enzyme kinetic data, and four were allometric methods, in which the respective human prediction was derived from animal studies. Obach et al. (1997) concluded that there is no single method to exactly predict human in vivo pharmacokinetic parameters from in vitro data, but many of the tested methods yielded a satisfactory level of accuracy to warrant decision-making in the drug discovery process. Generally, for the compounds that were highly protein-bound, the predicted clearance was underestimated, if the degree of binding was taken into account. Especially for the prediction of the volume of distribution, the plasma protein-binding factor must be included in the calculations. It should be noted that if an NCE binds extensively to plasma protein, it is most probable that it also binds to microsomal proteins. On the whole, the presented methods for estimating in vivo pharmacokinetic values from in vitro data provide a certain window of accuracy. For example, the estimation of t from in vitro enzyme kinetic data gives results accurate enough for the purpose of finding out the dosage regimens for an NCE.

2.3.2.4. Extrapolation of Cl_int to in vivo clearance in the whole organism

When extrapolation of Cl_int to the in vivo clearance in the whole organism is done, some preliminary information or assumptions are needed. These are presented in, for example, reviews by Ito et al. (1998a, b; Obach 1997). If the studied compound is metabolised via more than one pathway, the intrinsic clearances of these pathways need to be summed up to achieve a total Cl_int for the study system (microsomes, whole-cell systems, liver slices):

Cl_{int 1} + Cl_{int 2} + Cl_{int 3} ... + Cl_{int n} = Cl_{int tot}, where

1, 2, 3, ... , n represents different metabolic pathways. The assumptions needed for scaling to the clearance of the whole organism are the amount of microsomal protein per gram of liver wet weight, the wet weight of the whole liver of the organism, the liver blood flow and the weight of the organism. Information of distribution volume is also needed. If some organ other than the liver, such as the kidneys or the intestine, will participate significantly in the elimination of the studied compound, their Cl_organ has to be taken into account when scaling to the clearance of the whole organism.

2.3.2.5. Apparent K_i and type of inhibition

It is important to determine the apparent inhibition constant K_i for a compound that inhibits the metabolism of an NCE, for it is used in in vivo interaction predictions (Ito et al. 1998a). The use of initial velocity conditions in this series of assays is extremely important because conditions that do not fulfil the linear velocity demand would lead to an underestimation of the inhibitory potency of an NCE (Yuan et al. 1999).

The determination of the apparent K_i value is done either by fitting lines by linear regression analysis into the Dixon plot or any secondary plot, or by an iterative non-linear curve fitting and calculations based on the known Michaelis-Menten kinetics for the type of inhibition (Boobis 1995).

2.3.2.6. Prediction of drug-drug interactions

Drug-drug interactions that may alter pharmacokinetics could occur at several sites, including gastrointestinal absorption, plasma and/or tissue protein binding, transporter proteins, and metabolism (Ito et al. 1998b). The prediction of hepatic clearance is an important prerequisite for the prediction of drug-drug interactions, and the accuracy of the prediction method is dependent on the accuracy of the clearance prediction. The interaction prediction is complicated if there are multiple CYPs participating the biotransformation of the NCE. In that case, the relative contribution of each enzyme has to be taken into account (Obach et al. 1997).

Also, the type of inhibition (competitive, noncompetitive or uncompetitive) of the NCE is a valuable item of information. Independently of the inhibition type - except in the case of uncompetitive inhibition - when the substrate concentration is much lower than K_m, the degree of inhibition (R) is expressed as follows:

This is usually the case in therapeutic use (Ito et al. 1998b).

The determination of the inhibitor concentration in vivo is very difficult (or impossible), and the unbound concentration of an inhibitor is therefore usually utilised when calculating the degree of inhibition. However, as discussed above, the total concentration may be more appropriate to use in these calculations (Obach et al. 1997). The interindividual variation should also be considered, though it is problematic to take into account when extrapolating in vivo from in vitro studies (Ito et al. 1998a, 1998b).

When the inhibition of a CYP enzyme causes interactions, it has to be examined both from the point of view how the NCE affects other drugs administered simultaneously and how the other drugs affect the metabolism or therapeutic effect of the NCE. Clinically, if the half-lives of simultaneously administered drugs were equal or nearly equal, it would be possible to schedule the dosing regimens in such a way that the drugs do not interfere with each other’s effects (Obach et al. 1997). If an NCE inhibits the activity of some CYP enzymes, the in vivo concentrations of the drugs metabolised by these CYPs might increase dangerously. This was the case with mibefradil, which is a potent inhibitor of both the drug-transporting P-glycoprotein and CYP3A in vitro (Siepmann et al. 1995; Krahenbuhl et al. 1998; Mullins et al. 1998; Spoendlin et al. 1998; Prueksaritanont et al. 1999; Wandel et al. 2000). When the CYP enzymes catalysing the oxidative reactions of an NCE are identified, there will already exist some candidates for inhibiting the reactions. For example, if an NCE is metabolised predominantly by CYP3A4, it is most probable that classical CYP3A4 inhibitors such as azole antimycotics (for example Varhe et al. 1994; von Moltke et al. 1996) or grapefruit juice (see for example Proppe et al. 1995; Armeer & Weintraub 1997; Kivistö et al. 1999), could cause an elevation in the in vivo concentrations of the NCE.